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Prime Numbers and Encryption

Want to make   $250 000 ?  Find a big prime number, a really big one. It turns out there are organizations  ready to dough out good cash for a really large prime number.  This is because primes are used in   RSA cryptography . RSA Algorithm Let's look at the algorithm: 1.       Multiply two large prime numbers  p  and  q  to get the product  N 2.       Find two numbers  e  and  d , such that  ed = 1mod((p-1)(q-1)) , where  e  and  N  are relatively prime meaning they do not share any prime factors. 3.       Let's call  M  the original message and  C  the ciphered message:  a.       To encrypt: C = M e mod(N) b.       To decipher: M = C d mod(N)  In essence, using the public key   ( N,e)  will transform the original message   M   to the ciphered message  C . On the contrary, applying the private key  d  on the ciphered message   C  will result in the original message   M .  Security of Encryption The beauty of RSA is your public key can be published for anyone to

The Colours of Water - From The Caribbean to the South Pacific

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Last year, I took a number of vacations which involved cruising, diving, snorkelling and walking on glaciers. Thinking back on those trips, I could not help but notice that water and ice exhibited different colours in different settings.  I decided to dive deeper into the colours of water. Finally, here are my findings. Water’s True Colour The colour of an object mainly depends on the colour of light emitted from it. In the case of water its colour is also affected by factors like light source, absorption, scattering, and suspended materials. Absorption by water is stronger for red light, but weaker for blue light. Water is therefore, intrinsically blue. However, this effect is only apparent when the water is reasonably deep. This is why a glass of water appears colourless whereas a big aquarium looks bluish through the thickness of water. Why is the Sea Blue? I did two cruises last year, one in the Caribbean and the other in the South Pacific. Owing to the depth of the water, th

2011 New Year Resolutions

Happy New Year!  I fell prey once again to the 9 - 5 in December. Combined with the year end holiday season,  this blog saw very little action last month. However, my resolution this year is to post one article each week to make this blog an interesting read for all of you out there! I know they say that resolutions are made to be broken, but I have a great feeling about this one. See you all next week! -PTS

Next Generation Computers

I have not reposted for some time, but this article struck a chord with my early studies in computer engineering.  It highlights the limitations of Moore's Law and explores possible technologies for producing next gen computers!   I believe a new crop of chips replacing silicon will be invented one day, probably within the next ten years!  Mankind has always stepped up to the plate and performed in the face of a challenge.  Just look at the invention of the steam engine, the airplane, the rocket, and just how far we have come from the ENIAC  in the 1940's to where we are in the evolution of computers. -PTS

Moons in the Solar System (2 of 2)

Our Moon was thought to be the only one in the solar system until Galileo discovered four celestial objects orbiting Jupiter through his telescope back in 1610. Today, we know there are many more moons in the Solar System.  Here are some that are special: Saturn's Rings Saturn's thirty plus rings are technically made of billions of moons.  They can be as small as a pebble and as big as a city.  The rings of Saturn were believed to have formed when comets pushed Saturn's early moons too close for comfort.  Those moons were ripped and shredded into pieces by Saturn's gravity, eventually forming rings of rocks and ice debris around the planet. Enceladus (Saturn) Enceladus is Saturn's sixth largest moon and is only 300 miles across.  It is one of the brightest objects in the Solar System, reflecting almost all light from the sun thanks to its ice covered surface. Saturn's gravity acts on  Enceladus' core to create active volcanic eruptions. Surprisingly the

Moons in the Solar System (1 of 2)

Moons are interesting celestial bodies.  Until recent years, they are often overlooked in favour of other astronomical objects like stars and planets.  So what really is a moon?  By definition,  a moon is a natural satellite that orbits a planet.   It is important to note that gravity plays a role in shaping a planet's moons. Too much gravity and the moon is destroyed. Too little of it and the moon floats away until is no longer a moon. In this and the next articles, we will focus on the  moons in our Solar System. Let's start with the one we know best! Earth's Moon and the Giant Impact Hypothesis Several theories have been postulated on the formation of our moon. T he  Apollo mission was sent to the moon in 1969 during which rock samples were secured. These moon rocks were found to be almost identical to those of Earth's crust.  The catch however, is that the rocks were super heated. How could this be?   The story goes that Earth was actually hit by a Mars-sized pl

Life on Mars

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The 9 to 5 has prevented me from hitting full throttle on my blogging endeavours the last few months.  I may finally have struck a balance between work and blogging.  Over the next few months, I am going to write a number of posts on my favourite topic: The Universe . To start, let's look at the possibility of life on Mars.  The red planet has long been suggested as the next best rock in our Solar System to host life.  By that, I am not suggesting human-like Martians that you see on TV or the big screen (as this famous Martian image alludes). Instead it is quite likely that simple organisms might have existed back when Mars was more Earth-like. Here are some engaging arguments:  Mars water-scarred terrain - the planet has vast systems of canyons.  In fact, the "Grand Canyon" of Mars is 5 times longer and 4 times deeper than the one in the U.S. These rugged terrains suggest the forces of water and glacial ice once at work. Needless to say, water is a key breeding ground